A340842 Emirps p such that p + (sum of digits of p) is an emirp.
13, 71, 97, 701, 1061, 1223, 1597, 1847, 1933, 3067, 3089, 3373, 3391, 3889, 7027, 7043, 7577, 9001, 9241, 9421, 10061, 10151, 10333, 10867, 11057, 11657, 11677, 11897, 11923, 12227, 12269, 12809, 13147, 13457, 13477, 14087, 14207, 16979, 17011, 17033, 17903, 32173, 32203, 32353, 32687, 33589
Offset: 1
Examples
a(3) = 97 is an emirp because 97 and 79 are distinct primes. Its sum of digits is 9+7=16, and 97+16 = 113 is an emirp because 113 and 311 are primes.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
revdigs:= proc(n) local L,i; L:= convert(n,base,10); add(10^(i-1)*L[-i],i=1..nops(L)) end proc: isemirp:= proc(n) local r; if not isprime(n) then return false fi; r:= revdigs(n); r <> n and isprime(r) end proc: filter:= n -> isemirp(n) and isemirp(n +convert(convert(n,base,10),`+`)): select(filter, [seq(i,i=3..10^5,2)]);
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Python
from sympy import isprime def sd(n): return sum(map(int, str(n))) def emirp(n): if not isprime(n): return False revn = int(str(n)[::-1]) if n == revn: return False return isprime(revn) def ok(n): return emirp(n) and emirp(n + sd(n)) def aupto(nn): return [m for m in range(1, nn+1) if ok(m)] print(aupto(18000)) # Michael S. Branicky, Jan 24 2021